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A056824 Numbers of the form p^(2k+1), p prime, k >= 1. 6

%I #25 Dec 23 2020 04:10:07

%S 8,27,32,125,128,243,343,512,1331,2048,2187,2197,3125,4913,6859,8192,

%T 12167,16807,19683,24389,29791,32768,50653,68921,78125,79507,103823,

%U 131072,148877,161051,177147,205379,226981,300763,357911,371293,389017

%N Numbers of the form p^(2k+1), p prime, k >= 1.

%H Charles R Greathouse IV, <a href="/A056824/b056824.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ n^3 log^3 n. - _Charles R Greathouse IV_, Jan 15 2015

%F Sum_{n>=1} 1/a(n) = Sum_{p prime} 1/(p*(p^2-1)) = 0.2214633713... - _Amiram Eldar_, Dec 23 2020

%o (PARI) is(n)=my(e=isprimepower(n)); e>1 && e%2 \\ _Charles R Greathouse IV_, Jan 15 2015

%o (PARI) list(lim)=my(v=List(apply(k->k^3, primes([2,sqrtnint(lim\1,3)]))),t); forstep(e=5,log(lim+.5)\log(2),2, forprime(p=2,,t=p^e; if(t>lim, break); listput(v,t))); Set(v) \\ _Charles R Greathouse IV_, Jan 15 2015

%Y Cf. A025475, A000961.

%K nonn

%O 1,1

%A _Labos Elemer_, Aug 29 2000

%E Name edited by _Altug Alkan_, following a suggestion by _Felix Fröhlich_, May 17 2018

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)